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人教版高中數(shù)學選修3全概率公式教學設計
2.某小組有20名射手，其中1，2，3，4級射手分別為2，6，9，3名.又若選1，2，3，4級射手參加比賽，則在比賽中射中目標的概率分別為0.85，0.64，0.45，0.32，今隨機選一人參加比賽，則該小組比賽中射中目標的概率為________. 【解析】設B表示“該小組比賽中射中目標”，Ai(i=1，2，3，4)表示“選i級射手參加比賽”，則P(B)= P(Ai)P(B|Ai)= 2/20×0.85+ 6/20 ×0.64+ 9/20×0.45+ 3/20×0.32=0.527 5.答案：0.527 53.兩批相同的產(chǎn)品各有12件和10件，每批產(chǎn)品中各有1件廢品，現(xiàn)在先從第1批產(chǎn)品中任取1件放入第2批中，然后從第2批中任取1件，則取到廢品的概率為________. 【解析】設A表示“取到廢品”，B表示“從第1批中取到廢品”，有P(B)= 112，P(A|B)= 2/11 ，P(A| )= 1/11所以P(A)=P(B)P(A|B)+P( )P(A| )4．有一批同一型號的產(chǎn)品，已知其中由一廠生產(chǎn)的占 30%, 二廠生產(chǎn)的占 50% , 三廠生產(chǎn)的占 20%, 又知這三個廠的產(chǎn)品次品率分別為2% , 1%, 1%，問從這批產(chǎn)品中任取一件是次品的概率是多少？
人教版高中數(shù)學選修3條件概率教學設計
(2)方法一:第一次取到一件不合格品,還剩下99件產(chǎn)品,其中有4件不合格品,95件合格品,于是第二次又取到不合格品的概率為4/99,由于這是一個條件概率,所以P(B|A)=4/99.方法二:根據(jù)條件概率的定義,先求出事件A,B同時發(fā)生的概率P(AB)=(C_5^2)/(C_100^2 )=1/495,所以P(B|A)=(P"(" AB")" )/(P"(" A")" )=(1/495)/(5/100)=4/99.6.在某次考試中,要從20道題中隨機地抽出6道題,若考生至少答對其中的4道題即可通過;若至少答對其中5道題就獲得優(yōu)秀.已知某考生能答對其中10道題,并且知道他在這次考試中已經(jīng)通過,求他獲得優(yōu)秀成績的概率.解:設事件A為“該考生6道題全答對”,事件B為“該考生答對了其中5道題而另一道答錯”,事件C為“該考生答對了其中4道題而另2道題答錯”,事件D為“該考生在這次考試中通過”,事件E為“該考生在這次考試中獲得優(yōu)秀”,則A,B,C兩兩互斥,且D=A∪B∪C,E=A∪B,由古典概型的概率公式及加法公式可知P(D)=P(A∪B∪C)=P(A)+P(B)+P(C)=(C_10^6)/(C_20^6 )+(C_10^5 C_10^1)/(C_20^6 )+(C_10^4 C_10^2)/(C_20^6 )=(12" " 180)/(C_20^6 ),P(E|D)=P(A∪B|D)=P(A|D)+P(B|D)=(P"(" A")" )/(P"(" D")" )+(P"(" B")" )/(P"(" D")" )=(210/(C_20^6 ))/((12" " 180)/(C_20^6 ))+((2" " 520)/(C_20^6 ))/((12" " 180)/(C_20^6 ))=13/58,即所求概率為13/58.
人教版高中數(shù)學選修3正態(tài)分布教學設計
3.某縣農(nóng)民月均收入服從N(500,202)的正態(tài)分布,則此縣農(nóng)民月均收入在500元到520元間人數(shù)的百分比約為 . 解析:因為月收入服從正態(tài)分布N(500,202),所以μ=500,σ=20,μ-σ=480,μ+σ=520.所以月均收入在[480,520]范圍內(nèi)的概率為0.683.由圖像的對稱性可知,此縣農(nóng)民月均收入在500到520元間人數(shù)的百分比約為34.15%.答案:34.15%4.某種零件的尺寸ξ(單位:cm)服從正態(tài)分布N(3,12),則不屬于區(qū)間[1,5]這個尺寸范圍的零件數(shù)約占總數(shù)的 . 解析:零件尺寸屬于區(qū)間[μ-2σ,μ+2σ],即零件尺寸在[1,5]內(nèi)取值的概率約為95.4%,故零件尺寸不屬于區(qū)間[1,5]內(nèi)的概率為1-95.4%=4.6%.答案:4.6%5. 設在一次數(shù)學考試中,某班學生的分數(shù)X~N(110,202),且知試卷滿分150分,這個班的學生共54人,求這個班在這次數(shù)學考試中及格(即90分及90分以上)的人數(shù)和130分以上的人數(shù).解:μ=110,σ=20,P(X≥90)=P(X-110≥-20)=P(X-μ≥-σ),∵P(X-μσ)≈2P(X-μ130)=P(X-110>20)=P(X-μ>σ),∴P(X-μσ)≈0.683+2P(X-μ>σ)=1,∴P(X-μ>σ)=0.158 5,即P(X>130)=0.158 5.∴54×0.158 5≈9(人),即130分以上的人數(shù)約為9人.
人教版高中數(shù)學選修3組合與組合數(shù)教學設計
解析:因為減法和除法運算中交換兩個數(shù)的位置對計算結(jié)果有影響,所以屬于組合的有2個.答案:B2.若A_n^2=3C_(n"-" 1)^2,則n的值為( )A.4 B.5 C.6 D.7 解析:因為A_n^2=3C_(n"-" 1)^2,所以n(n-1)=(3"(" n"-" 1")(" n"-" 2")" )/2,解得n=6.故選C.答案:C 3.若集合A={a1,a2,a3,a4,a5},則集合A的子集中含有4個元素的子集共有 個. 解析:滿足要求的子集中含有4個元素,由集合中元素的無序性,知其子集個數(shù)為C_5^4=5.答案:54.平面內(nèi)有12個點,其中有4個點共線,此外再無任何3點共線,以這些點為頂點,可得多少個不同的三角形?解:(方法一)我們把從共線的4個點中取點的多少作為分類的標準:第1類,共線的4個點中有2個點作為三角形的頂點,共有C_4^2·C_8^1=48(個)不同的三角形;第2類,共線的4個點中有1個點作為三角形的頂點,共有C_4^1·C_8^2=112(個)不同的三角形;第3類,共線的4個點中沒有點作為三角形的頂點,共有C_8^3=56(個)不同的三角形.由分類加法計數(shù)原理,不同的三角形共有48+112+56=216(個).(方法二 間接法)C_12^3-C_4^3=220-4=216(個).
人教A版高中數(shù)學必修一用二分法求方程的近似解教學設計（1）
《數(shù)學1必修本（A版）》的第五章4.5.2用二分法求方程的近似解．本節(jié)課要求學生根據(jù)具體的函數(shù)圖象能夠借助計算機或信息技術(shù)工具計算器用二分法求相應方程的近似解，了解這種方法是求方程近似解的常用方法，從中體會函數(shù)與方程之間的聯(lián)系；它既是本冊書中的重點內(nèi)容，又是對函數(shù)知識的拓展，既體現(xiàn)了函數(shù)在解方程中的重要應用，同時又為高中數(shù)學中函數(shù)與方程思想、數(shù)形結(jié)合思想、二分法的算法思想打下了基礎，因此決定了它的重要地位．發(fā)展學生數(shù)學直觀、數(shù)學抽象、邏輯推理和數(shù)學建模的核心素養(yǎng)。課程目標 學科素養(yǎng)1.通過具體實例理解二分法的概念及其使用條件．2.了解二分法是求方程近似解的常用方法，能借助計算器用二分法求方程的近似解．3.會用二分法求一個函數(shù)在給定區(qū)間內(nèi)的零點，從而求得方程的近似解． a.數(shù)學抽象：二分法的概念；b.邏輯推理：運用二分法求近似解的原理；
人教版高中數(shù)學選修3二項式系數(shù)的性質(zhì)教學設計
1.對稱性與首末兩端“等距離”的兩個二項式系數(shù)相等,即C_n^m=C_n^(n"-" m).2.增減性與最大值 當k(n+1)/2時,C_n^k隨k的增加而減小.當n是偶數(shù)時,中間的一項C_n^(n/2)取得最大值;當n是奇數(shù)時,中間的兩項C_n^((n"-" 1)/2) 與C_n^((n+1)/2)相等,且同時取得最大值.探究2.已知(1+x)^n =C_n^0+C_n^1 x+...〖+C〗_n^k x^k+...+C_n^n x^n 3.各二項式系數(shù)的和C_n^0+C_n^1+C_n^2+…+C_n^n=2n.令x=1 得(1+1)^n=C_n^0+C_n^1 +...+C_n^n=2^n所以，(a+b)^n 的展開式的各二項式系數(shù)之和為2^n1. 在(a+b)8的展開式中,二項式系數(shù)最大的項為 ,在(a+b)9的展開式中,二項式系數(shù)最大的項為 . 解析:因為(a+b)8的展開式中有9項,所以中間一項的二項式系數(shù)最大,該項為C_8^4a4b4=70a4b4.因為(a+b)9的展開式中有10項,所以中間兩項的二項式系數(shù)最大,這兩項分別為C_9^4a5b4=126a5b4,C_9^5a4b5=126a4b5.答案:1.70a4b4 126a5b4與126a4b5 2. A=C_n^0+C_n^2+C_n^4+…與B=C_n^1+C_n^3+C_n^5+…的大小關(guān)系是( )A.A>B B.A=B C.A<B D.不確定 解析:∵(1+1)n=C_n^0+C_n^1+C_n^2+…+C_n^n=2n,(1-1)n=C_n^0-C_n^1+C_n^2-…+(-1)nC_n^n=0,∴C_n^0+C_n^2+C_n^4+…=C_n^1+C_n^3+C_n^5+…=2n-1,即A=B.答案:B
人教版高中數(shù)學選修3離散型隨機變量及其分布列(1)教學設計
4.寫出下列隨機變量可能取的值，并說明隨機變量所取的值表示的隨機試驗的結(jié)果．(1)一個袋中裝有8個紅球，3個白球，從中任取5個球，其中所含白球的個數(shù)為X.(2)一個袋中有5個同樣大小的黑球，編號為1,2,3,4,5，從中任取3個球，取出的球的最大號碼記為X.(3). 在本例(1)條件下，規(guī)定取出一個紅球贏2元，而每取出一個白球輸1元，以ξ表示贏得的錢數(shù)，結(jié)果如何？[解] (1)X可取0,1,2,3.X＝0表示取5個球全是紅球；X＝1表示取1個白球，4個紅球；X＝2表示取2個白球，3個紅球；X＝3表示取3個白球，2個紅球．(2)X可取3,4,5.X＝3表示取出的球編號為1,2,3；X＝4表示取出的球編號為1,2,4；1,3,4或2,3,4.X＝5表示取出的球編號為1,2,5；1,3,5；1,4,5；2,3,5；2,4,5或3,4,5.(3) ξ＝10表示取5個球全是紅球；ξ＝7表示取1個白球，4個紅球；ξ＝4表示取2個白球，3個紅球；ξ＝1表示取3個白球，2個紅球．
人教A版高中數(shù)學必修一兩角和與差的正弦、余弦和正切公式教學設計（2）
本節(jié)內(nèi)容是三角恒等變形的基礎，是正弦線、余弦線和誘導公式等知識的延伸，同時，它又是兩角和、差、倍、半角等公式的“源頭”。兩角和與差的正弦、余弦、正切是本章的重要內(nèi)容，對于三角變換、三角恒等式的證明和三角函數(shù)式的化簡、求值等三角問題的解決有著重要的支撐作用。 課程目標1、能夠推導出兩角和與差的正弦、余弦、正切公式并能應用; 2、掌握二倍角公式及變形公式，能靈活運用二倍角公式解決有關(guān)的化簡、求值、證明問題．數(shù)學學科素養(yǎng)1.數(shù)學抽象：兩角和與差的正弦、余弦和正切公式； 2.邏輯推理： 運用公式解決基本三角函數(shù)式的化簡、證明等問題；3.數(shù)學運算：運用公式解決基本三角函數(shù)式求值問題.4.數(shù)學建模：學生體會到一般與特殊，換元等數(shù)學思想在三角恒等變換中的作用。.
人教版高中英語必修3Festivals around the World說課稿3篇
Teaching plan for Unit 1 book3Good morning, teachers. It’s my great pleasure to be here because I can share my lesson with you and I can learn a lot from it. I’ll begin my lesson from the following four parts， the teaching material, the teaching methods, the studying methods and the teaching procedure.Firstly, let me talk about the teaching material. The content of my lesson is the reading passage festivals and celebrations of Unit 1 Festivals around the world. This passage is about festivals and celebrations. By studying this passage, we’ll enable the students to know that festivals exit everywhere, and many of festivals in different countries celebrate similar ideas. As we all know, the reading passage is the center of each unit. If the Ss can learn it well, it will be helpful to make the Ss learn the rest of this unit.After studying the teaching material, I think the teaching aims are as the followings:1. Knowledge aims:(1) The Ss can master the usage of the important words andexpressions.(2)The Ss can use the __________________ (grammar) in the proper situation.Make students know about the festivals all over the world and the detail of the festivals, such as origin, content, and the date of the holiday festivals.2. Ability aims:(1) Students can talk about festivals and celebrations in English(2) To improve the student’s reading ability, especially their skimming and scanning ability.3. Emotion aims:Make the Ss know about the foreign festivals, and respect other countries’ custom.Next, let’s come to the important points and the difficult points.The important point is how to make the Ss understand the text better and the difficult point is how can they talk about it. secondly， Teaching Methods:1. task-based Language Teaching2. Computer assisted language teaching.3. question-and–answer methodThirdly， Studying Methods:
新人教版高中英語必修2Unit 1 Cultural Heritage-Discovering Useful Structure教案二
This theme of the part is “ Describe people or things in greater detail”. Students have learned the grammar(restrictive relative clauses) in Book 1, and further review and consolidate its structure “prep+relative pronouns(which/whom)” and the relative adverbs(when, where and why), besides students should understand its form, meaning and functions. In this section, students should be able to express the grammar correctly in daily communication and in the writing. 1. Review the basic usages of relative pronouns and adverbs of attributive clauses . 2. Learn to use some special cases about restrictive relative clauses.3. Learn to write sentences with restrictive relative clauses flexibly according to the context.1. Review the basic usages of relative pronouns and adverbs of attributive clauses .2. Learn to use some special cases about restrictive relative clauses.3. Learn tow rite sentences with restrictive relative clauses flexibly according to the context.Step 1. Observe the following sentences, and mark the relative pronouns and the adverbs. 1. After listening to the scientists who had studied the problems, and citizens who lived near the dam, the government turned to the United Nations for help.2. Temples and other cultural sites were taken down piece by piece, and then moved and put back together again in a place where they were safe from the water.Step 2 PracticePlease complete these sentences with relative pronouns and relative adverbs and answer the following questions.Questions: 1. What is the head noun ?2. What relative words should be used ?3. What elements do they act in these sentences ?
新人教版高中英語必修2Unit 1 Cultural Heritage-Reading and Thinking教案二
1. This section focuses on "Understanding how a problem was solved”, which is aimed to guide students to analyze and discuss the challenges and problems faced by cultural heritage protection during the construction of Aswan Dam, as well as the solutions. On the basis of understanding, students should pay attention to the key role of international cooperation in solving problems, and attach importance to the balance and coordination between cultural heritage protection and social and economic development. Students are encouraged to face challenges actively, be good at cooperation, and make continuous efforts to find reasonable ways and means to solve problems.2. Enable students to understand the main information and text structure of the reading text;3. Motivate students to use the reading strategy "make a timeline" according to the appropriate text genre;4. Enable students to understand how a problem was solved;5. Enable students to understand the value of protecting cultural heritage by teamwork and global community;1. Guide students to pay attention to reading strategies, such as prediction, self-questioning and scanning.2. Help students sort out the topic language about protecting cultural relics and understand the narrative characteristics of "time-event" in illustrative style3. Lead students to understand the value of protecting cultural heritage by teamwork and global community;
新人教版高中英語必修2Unit 3 The Internet-Listening &Speaking＆Talking教案二
From the pictures in the text and the title--- choose the best app, we can know that this part is about how to save money by using apps.Step 2 While-listening1. Laura and Xiao Bo are talking about apps. Listen to their conversation and find out what apps they want.Xiao Bo is looking for a(n) exercise app to help him get in shape.Laura would like an app for getting rich and another that will make her grades better.2. Listen again. Are the sentences true T or false F?1). Both of Xiao Bo's apps keep track of the steps he takes._____2). Xiao Bo's second app can help him make a fitness plan._____3). Laura needs an app that will help her get discounts.______4). Laura needs an app that will add money to her bank account._______F T F T3. Listen once more and tick the sentence you hear. Underline the words used to express predictions, guesses, and beliefs.Predictions, Guesses, and Beliefs________It might help me walk more.________My guess is that it wouldn't work.________I imagine this app would help me get fit faster________I suppose that would be good.________I guess you could save a little with this app.________I suppose there would be some problems, too.________I believe this app could help me get thinner.
新人教版高中英語必修2Unit 3 The Internet-Discovering Useful Structure教案二
This teaching period mainly deals with grammar “The Present Perfect Passive Voice.” To begin with, teachers should lead students to revise what they have learned about the Present Perfect Passive Voice. And then, teachers move on to stress more special cases concerning this grammar。This period carries considerable significance to the cultivation of students’ writing competence and lays a solid foundation for the basic appreciation of language beauty. The teacher is expected to enable students to master this period thoroughly and consolidate the knowledge by doing some exercises. 1. Guide students to review the basic usages of the Present Perfect Passive Voice2. Lead students to learn to use some special cases concerning the Present Perfect Passive Voice flexibly.2. Enable students to use the basic phrases structures flexibly.3. Strengthen students’ great interest in grammar learning.1. Help students to appreciate the function of the Present Perfect Passive Voice in a sentence2. Instruct students to write essays using the proper the Present Perfect Passive Voice.觀察下列句子特點，總結(jié)共同點。1．(教材P28)Much has been written about the wonders of the World Wide Web．2．(教材P28)But the Internet has done much more for people than simply make life more convenient．3．(教材P28)Many people have been helped by the club．4．(教材P28)She no longer feels lonely, and her company has become quite successful．5．(教材P32)Today I thought I’d blog about a question that has been asked many times—how do you stay safe online and avoid bad experiences on the Internet?
新人教版高中英語必修2Unit 3 The Internet-Reading for Writing教案二
8. However, the more polite you are, the less likely it is you will be attacked. 然而, 你越有禮貌, 你被攻擊的可能性就越小。 Step 8 Writing---the articleHow to stay safe in the online chat roomToday I thought I’d blog about a question that has been asked many times--- how do you stay safe online and avoid bad experiences in the online chat room ? I’m not an expert, but many years as a blogger have taught me a thing or two.First of all, there’s the golden rule of the Internet: keep out of what makes you uneasy. Don’t post comments or click on anything. Second, protect your privacy. Don’t give out too much private information like your address, phone numbers, the ID numbers, etc. Third, be polite. If you are polite to others on the Internet, you won’t be attacked in normal situation. Finally, don’t believe in others easily and never meet someone you met online alone. It is very dangerous.Have you had any bad experiences online, or do you have some good advice for staying safe? Post your comments below!Step 9 Pair workExchange drafts with a partner. Use this checklist to help your partner revise his/her draft.1. Does the writer tell the reader what he/she know about the topic ?2. Are the tips and suggestions well organised ?3. Has the writer defined the new words ?4. Does the author include examples, comparison, or explanations ?5. Does the writer end by asking readers to leave comments and/or suggestions ?6. Can you find any grammar or spelling mistakes.Step 6 HomeworkPut up your revised draft in the classroom or read it to your class.
新人教版高中英語必修2Unit 3 The Internet-Reading and Thinking教案二
Q5：What's Jan's next goal?Her next goal is to start a charity website to raise money for children in poor countries.Q6：What can we learn from her experiences?We learn that when we go through tough times, we can find help and support from other people online. We learn that we can feel less lonelyStep 5: While reading---rethinkingQ1: What is Jan’s attitude to the Internet ?Thankful/Grateful, because it has changed her and her life.Q2: What writing skills is used in the article ?Examples(Jan’s example, the 59-year-old man’s and the 61-year-old woman’s example)Q3: Can you get the main idea of the article ?The Internet has changed Jan’s life/Jan’s life has been changed by the Internet.Step 6 Post reading---Retell the storyMuch has been written about the wonders of the World Wide Web. There are countless articles (1)telling(tell) us how the Internet has made our lives more convenient. But the Internet has done a lot (2)more(much) for people than simply make life more convenient. People’s lives (3) have been changed(change) by online communities and social networks so far. Take Jan for example, who developed a serious illness that made her (4)stuck(stick) at home with only her computer to keep (5)her(she) company. She joined an online group (6)where she could share problems, support and advice with others. She considered the ability to remove the distance between people as one of the greatest (7)benefits(benefit). She was so inspired (8)that she started an IT club in which many people have been helped. She has started to learn more about how to use the Internet to make society better. Her next goal is to start a charity website to raise money (9)for children in poor countries. Jan’s life has been (10)greatly(great) improved by the Internet.
高中思想政治人教版必修三《文化創(chuàng)新的途徑》說課稿
二、說學情本課的教學對象為高二學生，他們思維活躍已具備一定歸納能力和分析、綜合能力，能夠自主地分析現(xiàn)實生活中的一些文化行為，但看問題往往比較偏激、片面，缺乏良好的邏輯思維能力。所以，在文化創(chuàng)新的途徑上要對他們進行指導，以免走入誤區(qū)。三、教學目標根據(jù)新課程標準、教材特點、學生的實際，我確定了如下教學目標：【知識與能力目標】1.理解文化創(chuàng)新的根本途徑和兩個基本途徑;2.了解文化創(chuàng)新過程中需要堅持正確方向，克服錯誤傾向。
人教A版高中數(shù)學必修一冪函數(shù)教學設計（2）
冪函數(shù)是在繼一次函數(shù)、反比例函數(shù)、二次函數(shù)之后，又學習了單調(diào)性、最值、奇偶性的基礎上，借助實例，總結(jié)出冪函數(shù)的概念，再借助圖像研究冪函數(shù)的性質(zhì).課程目標1、理解冪函數(shù)的概念，會畫冪函數(shù)y=x，y=x2，y=x3，y=x－1，y=x 的圖象；2、結(jié)合這幾個冪函數(shù)的圖象，理解冪函數(shù)圖象的變化情況和性質(zhì)；3、通過觀察、總結(jié)冪函數(shù)的性質(zhì)，培養(yǎng)學生概括抽象和識圖能力．數(shù)學學科素養(yǎng)1.數(shù)學抽象：用數(shù)學語言表示函數(shù)冪函數(shù)；2.邏輯推理：常見冪函數(shù)的性質(zhì)；3.數(shù)學運算：利用冪函數(shù)的概念求參數(shù)；4.數(shù)據(jù)分析：比較冪函數(shù)大?。?.數(shù)學建模：在具體問題情境中，運用數(shù)形結(jié)合思想，利用冪函數(shù)性質(zhì)、圖像特點解決實際問題。重點：常見冪函數(shù)的概念、圖象和性質(zhì)；難點：冪函數(shù)的單調(diào)性及比較兩個冪值的大?。?/p>
人教A版高中數(shù)學必修一單調(diào)性與最大（?。┲到虒W設計（1）
《函數(shù)的單調(diào)性與最大（?。┲祡》系人教A版高中數(shù)學必修第一冊第三章第二節(jié)的內(nèi)容,本節(jié)包括函數(shù)的單調(diào)性的定義與判斷及其證明、函數(shù)最大（?。┲档那蠓āＴ诔踔袑W習函數(shù)時,借助圖像的直觀性研究了一些函數(shù)的增減性,這節(jié)內(nèi)容是初中有關(guān)內(nèi)容的深化、延伸和提高函數(shù)的單調(diào)性是函數(shù)眾多性質(zhì)中的重要性質(zhì)之一,函數(shù)的單調(diào)性一節(jié)中的知識是前一節(jié)內(nèi)容函數(shù)的概念和圖像知識的延續(xù),它和后面的函數(shù)奇偶性,合稱為函數(shù)的簡單性質(zhì),是今后研究指數(shù)函數(shù)、對數(shù)函數(shù)、冪函數(shù)及其他函數(shù)單調(diào)性的理論基礎;在解決函數(shù)值域、定義域、不等式、比較兩數(shù)大小等具體問需用到函數(shù)的單調(diào)性;同時在這一節(jié)中利用函數(shù)圖象來研究函數(shù)性質(zhì)的救開結(jié)合思想將貫穿于我們整個高中數(shù)學教學。
人教版高中數(shù)學選修3離散型隨機變量及其分布列(2)教學設計
溫故知新 1.離散型隨機變量的定義可能取值為有限個或可以一一列舉的隨機變量,我們稱為離散型隨機變量.通常用大寫英文字母表示隨機變量,例如X,Y,Z;用小寫英文字母表示隨機變量的取值,例如x,y,z.隨機變量的特點: 試驗之前可以判斷其可能出現(xiàn)的所有值，在試驗之前不可能確定取何值；可以用數(shù)字表示2、隨機變量的分類①離散型隨機變量:X的取值可一、一列出；②連續(xù)型隨機變量:X可以取某個區(qū)間內(nèi)的一切值隨機變量將隨機事件的結(jié)果數(shù)量化．3、古典概型:①試驗中所有可能出現(xiàn)的基本事件只有有限個；②每個基本事件出現(xiàn)的可能性相等。二、探究新知探究1.拋擲一枚骰子,所得的點數(shù)X有哪些值？取每個值的概率是多少？ 因為X取值范圍是{1，2，3，4，5，6}而且"P(X=m)"=1/6,m=1,2,3,4,5,6.因此X分布列如下表所示
人教版高中數(shù)學選修3離散型隨機變量的方差教學設計
3.下結(jié)論.依據(jù)均值和方差做出結(jié)論.跟蹤訓練2. A、B兩個投資項目的利潤率分別為隨機變量X1和X2，根據(jù)市場分析， X1和X2的分布列分別為X1 2% 8% 12% X2 5% 10%P 0.2 0.5 0.3 P 0.8 0.2求：(1)在A、B兩個項目上各投資100萬元， Y1和Y2分別表示投資項目A和B所獲得的利潤，求方差D(Y1)和D(Y2)；(2)根據(jù)得到的結(jié)論，對于投資者有什么建議？ 解：(1)題目可知，投資項目A和B所獲得的利潤Y1和Y2的分布列為：Y1 2 8 12 Y2 5 10P 0.2 0.5 0.3 P 0.8 0.2所以 ;; 解：(2) 由(1)可知 ，說明投資A項目比投資B項目期望收益要高；同時 ，說明投資A項目比投資B項目的實際收益相對于期望收益的平均波動要更大.因此，對于追求穩(wěn)定的投資者，投資B項目更合適;而對于更看重利潤并且愿意為了高利潤承擔風險的投資者，投資A項目更合適.